To truly understand the snowflake's relationship to the flower we need some background.

The Hexagon / Hexagram

Six (6) is the number of structure. The hexagon is used for structure at all scales in the universe from the microcosm to the macrocosm. Snowflakes are always hexagonal.

Consider something as simple as coins or cylinders packing in hexagonal rows. 6 fit perfectly around a central 7th with all of them touching. This is really the essence of structure.

Many crystals other than ice have hexagonal crystal systems:

Even the gaseous planet Saturn has hexagonal clouds on its north pole discovered by Voyager 1 in 1977 and verified again in 2006 by the Cassini spacecraft, meaning this hexagon is a persistent structure on the scale of a planet. Think about that.

Saturn hexagonal north pole feature

In the microcosm living creatures such as bees create hexagonal houses and birthing chambers for their young. Hexagonal space frames make solid structures:

The Pentagon / Pentagram

Five (5) is the number of life. All trees bearing fruit we can eat have blossoms with 5 petals. Apples have pentagrams inside that you’ll discover if you ever cut one across its equator. Perhaps Eve cut her first apple this way and received a bit of knowledge from the old tree?

Man's body fits a pentagram and his parts are are interrelated with the golden proportion which is based on Phi.

Image by renaissance alchemist Heinrich Cornelius Agrippa

The pentagram encodes the golden number Phi within itself fractally.

Bridging Macrocosm and Microcosm, Life and Structure

The relationship between 6 and 5 is the key.

"He who joins the hexagram and pentagram has solved half of the sacred secret."Eliphas Levi (19th century magician)

Digital art by Scott Onstott

In order of increasing scale from microcosm to macrocosm, what follows are some relationships I've observed between 6 and 5. I would love to hear from you if you discover any more.

Mathematics

The relationship between Phi and Pi is as follows:

1.2 x 1.6180 x 1.6180 = 3.1415

This relationship isn't exact due to the transcendental nature of Pi. I see 6/5 more as a resonance built into the architecture of the universe.

The Daylight Standard
As you heat objects up they start to emit visible wavelengths appearing red, orange, yellow, white, and blue with increasing temperature. The average color of daylight is calibrated by a color temperature of 6500 degrees Kelvin (degrees above absolute zero). The International Commission on Illumination calls this standard Illuminant D65. Many professional photographers and graphic designers use D65 lamps for studio work where color accuracy is important.